In many cases the detailed knowledge of dynamic processes at the atomic level is essential to understand protein function, e.g., ligand binding or enzymatic reactions. Through a microscopic description of interatomic forces [1] and atomic motions, molecular dynamics (MD) simulations [2,3] can serve as a tool to interpret experimental data and to make predictions, which can guide future experiments. In such simulations, the motions are computed by numerically solving Newton's equations. Here, the forces are derived from an empirical energy function accounting for chemical binding forces as well as van der Waals and electrostatic interactions between partially charged atoms.
For the study of protein dynamics quite large simulation systems -- typically comprising several 10,000 atoms -- are required. The system must be that large because the native protein environment (water or lipids) strongly affects the dynamics of the protein [4,5,6,7,8] and, therefore, has to be included into the simulation system. The large number of atoms provides a first reason why MD simulations of proteins pose a computational challenge. A second reason is that femtosecond integration time steps are necessary to enable sufficiently smooth descriptions of the fastest degrees of freedom. Thus, MD simulations of such systems are currently limited to nanoseconds (i.e., a few million integration steps) even if the most powerful supercomputers and efficient algorithms are used. Although there are a number of biochemically important processes which occur at such very fast time scales and have been successfully studied by MD simulations [9,10], most biochemical processes occur at much slower scales and, therefore, are currently inaccessible to conventional MD methods. This technical limitation motivates substantial efforts taken by many groups to determine suitable approximations which ideally should allow more efficient simulations without seriously affecting relevant features of the system, which may be grouped into specialized integration schemes and multiple time stepping [11,12,13,,15,16,17,18,19,,21,22,23,24,25,,27,28,29,30,31] (see also the chapter by Schlick and Berne within this book), multipole methods [32,33,34,35,,37,38], as well as grid and Ewald methods [39,40,41,42]. Most of the efforts focus on the efficient computation of the electrostatic interactions within the protein and between protein and solvent [see also the chapter by W.v. Gunsteren et al. within this book], since, typically, this is the computationally most demanding task.
As an example for an efficient yet quite accurate approximation, in the first part of our contribution we describe a combination of a structure adapted multipole method with a multiple time step scheme (FAMUSAMM -- fast multistep structure adapted multipole method) and evaluate its performance. In the second part we present, as a recent application of this method, an MD study of a ligand-receptor unbinding process enforced by single molecule atomic force microscopy. Through comparison of computed unbinding forces with experimental data we evaluate the quality of the simulations. The third part sketches, as a perspective, one way to drastically extend accessible time scales if one restricts oneself to the study of conformational transitions, which are ubiquitous in proteins and are the elementary steps of many functional conformational motions.